Water depth decreases at 128/125π ft ^3/min when the cone leaks water at a rate of 10 ft3/min
The ratio of the radius(r) of the upper surface of the water to the water depth (w) is based on the overall dimensions of the cone r/w = 5/10.
The volume of a cone of water is given by the formula V(w) = (π/12)w^3
After differentiation we get dV/dW = π/4w^2
We are told that dV/dT = -3
dW/dT= (dW/dV)(dV/dT) = 4/πw^2(-3)
When the depth of water is 10 ft we get the rate of fall of water is 128/125π ft ^3/min.
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